Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform

• URL: http://arxiv.org/abs/2211.03635v1
• Date: Mon, 7 Nov 2022 15:46:00 GMT
• Title: Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform
• Authors: Huiru Xiao, Xin Liu, Yangqiu Song, Ginny Y. Wong, Simon See
• Abstract summary: The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings.
• Score: 29.205221688430733
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbolic embeddings do not deal with multi-relations. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings. To apply the geometric transformations which account for different relations and the attention mechanism in the complex hyperbolic space, we propose to use the fast Fourier transform (FFT) as the conversion between the real and complex hyperbolic space. Constructing the attention-based transformations in the complex space is very challenging, while the proposed Fourier transform-based complex hyperbolic approaches provide a simple and effective solution. Experimental results show that our methods outperform the baselines, including the Euclidean and the real hyperbolic embedding models.

Related papers

• Hyperbolic Delaunay Geometric Alignment [52.835250875177756]
  We propose a similarity score for comparing datasets in a hyperbolic space. The core idea is counting the edges of the hyperbolic Delaunay graph connecting datapoints across the given sets. We provide an empirical investigation on synthetic and real-life biological data and demonstrate that HyperDGA outperforms the hyperbolic version of classical distances between sets.
  arXiv  Detail & Related papers  (2024-04-12T17:14:58Z)
• Alignment and Outer Shell Isotropy for Hyperbolic Graph Contrastive Learning [69.6810940330906]
  We propose a novel contrastive learning framework to learn high-quality graph embedding. Specifically, we design the alignment metric that effectively captures the hierarchical data-invariant information. We show that in the hyperbolic space one has to address the leaf- and height-level uniformity which are related to properties of trees.
  arXiv  Detail & Related papers  (2023-10-27T15:31:42Z)
• Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning [77.1421343649344]
  We propose a generalization of Transformers towards operating entirely on the product of constant curvature spaces. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges.
  arXiv  Detail & Related papers  (2023-09-08T02:44:37Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Ultrahyperbolic Knowledge Graph Embeddings [41.85886045379838]
  We present an ultrahyperbolic KG embedding in an ultrahyperbolic (or pseudo-Riemannian) manifold. In particular, we model each relation as a pseudo-orthogonal transformation that preserves the pseudo-Riemannian bilinear form. Experimental results on three standard KGs show that UltraE outperforms previous Euclidean- and hyperbolic-based approaches.
  arXiv  Detail & Related papers  (2022-06-01T12:31:26Z)
• HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization [52.369435664689995]
  We introduce a textitHyperbolic Regularization powered Collaborative Filtering (HRCF) and design a geometric-aware hyperbolic regularizer. Specifically, the proposal boosts optimization procedure via the root alignment and origin-aware penalty. Our proposal is able to tackle the over-smoothing problem caused by hyperbolic aggregation and also brings the models a better discriminative ability.
  arXiv  Detail & Related papers  (2022-04-18T06:11:44Z)
• Enhancing Hyperbolic Graph Embeddings via Contrastive Learning [7.901082408569372]
  We propose a novel Hyperbolic Graph Contrastive Learning (HGCL) framework which learns node representations through multiple hyperbolic spaces. Experimental results on multiple real-world datasets demonstrate the superiority of the proposed HGCL.
  arXiv  Detail & Related papers  (2022-01-21T06:10:05Z)
• Unit Ball Model for Hierarchical Embeddings in Complex Hyperbolic Space [28.349200177632852]
  Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. We propose to learn the graph embeddings in the unit ball model of the complex hyperbolic space.
  arXiv  Detail & Related papers  (2021-05-09T16:09:54Z)
• A Hyperbolic-to-Hyperbolic Graph Convolutional Network [46.80564170208473]
  We propose a hyperbolic-to-hyperbolic graph convolutional network (H2H-GCN) that directly works on hyperbolic manifold. The H2H-GCN achieves substantial improvements on the link prediction, node classification, and graph classification tasks.
  arXiv  Detail & Related papers  (2021-04-14T16:09:27Z)
• Differentiating through the Fr\'echet Mean [51.32291896926807]
  Fr'echet mean is a generalization of the Euclidean mean. We show how to differentiate through the Fr'echet mean for arbitrary Riemannian manifold. This fully integrates the Fr'echet mean into the hyperbolic neural network pipeline.
  arXiv  Detail & Related papers  (2020-02-29T19:49:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.